[Troo]

1) Is 31,000¥ enough for 4 weeks food? I won't be eating at restaurants (except for sometimes lunch and breakfast where I've seen meals at mos burger etc. at about 290¥) and will mainly just be buying bento from department stores and making my own meals.

Buying fresh ingredients in Japan is notoriously more expensive than eating out. I'm not sure to what degree you'd like to be making your own meals (i.e. do you want to make your own dashi stock, or buy it pre-prepared? Do you want to even go to the level of using dashi, or will you buy pre-prepared meals to heat up?), but the above advice on how much it costs to eat seems good to me. I've got by on around 1,000 yen in a single day (bakery for breakfast, student-cheap ramen for lunch and dinner), but you really should allow about 1,000 yen for an evening meal, maybe 500 yen for lunch, and around 100-500 for breakfast (depending on what you like to eat for breakfast). Remember that having anything other than the free water will bump up the cost of a meal, so consider before requesting juice, coke, or coffee.

2)Is there a Tokyo version of the JR Pass? Like a month long all access pass to Tokyo railway lines for a month?

You can get a JR-East pass: JR-EAST:JR EAST PASS

Japan's rail networks are quite a convoluted affair. Along with the various Japan Rail divisions, there are a plethora of privately-owned rail lines. In inner-city Tokyo you won't really need JR lines at all. Transit is covered by buses and underground rail, of which there are two operators: Toei and Tokyo Metro. Both Toei and Metro offer a day pass which only covers that company's lines, but I have managed to buy a Metro day pass which included Toei lines for marginally less than buying the two day-passes separately would have cost. It's well worth knowing in advance how much travel you are likely to do that day to see whether it's worth the cost of the pass (around 900 yen), or whether single tickets will be cheaper.

If you'll be travelling out into the greater Tokyo area, then the majority of those lines are JR, and either a full JR pass or a JR-East will cover them.

3)How can I reserve a seat on the Keisei Ueno skyliner from the internet? (The Narita <--> Ueno skyliner) I've looked on their website and cant find out how to reserve a seat...

I wouldn't bother, to be honest. The Skyliner leaves Narita every ten minutes or so, and the chaps at the ticket counters speak reasonable English. You can also save yourself quite a few yen by using regular rail from Narita into Tokyo, and it only takes an extra half-hour. While the Skyliner is a nice, comfortable train, and cheaper than the Narita Express (which goes to Tokyo station, not Ueno), it's more expensive than the regular ole kaisoku services (which also go to Tokyo station).

I'd say it depends on:
- How long you've spent on the plane to NRT (is it a mere 5-hour hop, or a full-on 12-hour slog?)
- Whether or not you can sleep on planes
- How desperate you are to reach your hotel on arrival
- Where your hotel is, and which Tokyo terminal is easier

4)Recommendations of must see places in Tokyo

I heartily reccommend Sengakuji temple, although you need to use that pesky Toei subway to get to it